Afamily has four children. if the genders of these children are listed in the order they are born, there are sixteen possible outcomes: , bbbg, bbgb, bgbb, gbbb, bgbg, gbgb, bggb, gbbg, bbgg, ggbb, bggg, gbgg, ggbg, gggb, and . assume these outcomes are equally likely. let represent the number of children that are girls. find the probability distribution of .

Step-by-step explanation:

A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG.

Let X represent the number of children that are girls. Then

1. When X=0, there is one possible outcome BBBB. So

2. When X=1, then there are 4 possible outcomes GBBB, BGBB, BBGB, BBBG, so

3. When X=2, then there are 6 possible outcomes BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, so

4. When X=3, then there are 4 possible outcomes GGGB, GGBG, GBGG, BGGG, so

5. When X=4, then there is one possible outcome GGGG, so

Now, the probability distribution table is

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

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